De Morgan's laws

In set theory and Boolean algebra, these are written formally as

${\displaystyle {\begin{aligned}{\overline {A\cup B}}&={\overline {A}}\cap {\overline {B}},\\{\overline {A\cap B}}&={\overline {A}}\cup {\overline {B}},\end{aligned}}}$

where

• A and B are sets,
• A is the complement of A,
• ∩ is the intersection, and
• ∪ is the union.

Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician. He formulated De Morgan's laws and introduced the term mathematical induction, making its idea rigorous.

Augustus De Morgan
Augustus De Morgan (1806–1871)
Born	27 June 1806 Madurai, Madras Presidency, British Empire (present-day India)
Died	18 March 1871 (aged 64) London, England
Residence	India England
Nationality	British
Alma mater	Trinity College, Cambridge
Known for	De Morgan's laws De Morgan algebra Relation algebra Universal algebra
Scientific career
Fields	Mathematician and logician
Institutions	University College London University College School
Academic advisors	John Philips Higman George Peacock William Whewell
Notable students	Edward Routh James Joseph Sylvester Frederick Guthrie William Stanley Jevons Ada Lovelace Francis Guthrie Stephen Joseph Perry
Influences	George Boole
Influenced	Thomas Corwin Mendenhall Isaac Todhunter